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Semi-lattice of varieties of quasigroups with linearity
Репозиторій DSpace/Manakin
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Semi-lattice of varieties of quasigroups with linearity
Інший ID:
DOI:10.12958/adm1748
2020 MSC: Primary 20N05, 20N15, 39B52, 08A05; Secondary 05A15, 05B07
2020 MSC: Primary 20N05, 20N15, 39B52, 08A05; Secondary 05A15, 05B07
Посилання:
Semi-lattice of varieties of quasigroups with linearity / F.M. Sokhatsky, H.V. Krainichuk, V.A. Sydoruk // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 261–285. — Бібліогр.: 29 назв. — англ.
Підтримка:
The authors are grateful to the members of Scientific Ukrainian Mathematical School “Multiary Invertible Functions” (SUMS “MIF”) for their helpful discussions on the problem and to the English reviewer V. Obshanska.
Дата:
2021
Переглядів:
217
Завантажень:
81
Анотація:
A σ-parastrophe of a class of quasigroups 𝕬 is a class σ𝕬 of all σ-parastrophes of quasigroups from 𝕬. A set of all pairwise parastrophic classes is called a parastrophic orbit or a truss. A parastrophically closed semi-lattice of classes is a bunch. A linearity bunch is a set of varieties which contains the variety of all left linear quasigroups, the variety of all left alinear quasi-groups, all their parastrophes and all their intersections. It contains 14 varieties, which are distributed into six parastrophic orbits. All quasigroups from these varieties are called dilinear. To obtain all varieties from the bunch, concepts of middle linearity and middle alinearity are introduced. A well-known identity or a system of identities which describes a variety from every parastrophic orbit of the bunch is cited. An algorithm for obtaining identities which describe all varieties from the parastrophic orbits is given. Examples of quasigroups distinguishing one variety from the other are presented.
